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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pairplot: Visualizing High Dimensional Data\n",
    "\n",
    "This example provides how to visualize high dimensional data using the pairplot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import graspologic\n",
    "\n",
    "import numpy as np\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulate a binary graph using stochastic block model\n",
    "The 3-block model is defined as below:\n",
    "\n",
    "\\begin{align*}\n",
    "n &= [50, 50, 50]\\\\\n",
    "P &= \n",
    "\\begin{bmatrix}0.5 & 0.1 & 0.05 \\\\\n",
    "0.1 & 0.4 & 0.15 \\\\\n",
    "0.05 & 0.15 & 0.3\n",
    "\\end{bmatrix}\n",
    "\\end{align*}\n",
    "\n",
    "Thus, the first 50 vertices belong to block 1, the second 50 vertices belong to block 2, and the last 50 vertices belong to block 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from graspologic.simulations import sbm\n",
    "\n",
    "n_communities = [50, 50, 50]\n",
    "p = [[0.5, 0.1, 0.05], \n",
    "     [0.1, 0.4, 0.15], \n",
    "     [0.05, 0.15, 0.3],]\n",
    "\n",
    "np.random.seed(2)\n",
    "A = sbm(n_communities, p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Embed using adjacency spectral embedding to obtain lower dimensional representation of the graph\n",
    "\n",
    "The embedding dimension is automatically chosen. It should embed to 3 dimensions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from graspologic.embed import AdjacencySpectralEmbed\n",
    "\n",
    "ase = AdjacencySpectralEmbed()\n",
    "X = ase.fit_transform(A)\n",
    "\n",
    "print(X.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Use pairplot to plot the embedded data\n",
    "\n",
    "First we generate labels that correspond to blocks. We pass the labels along with the data for pair plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from graspologic.plot import pairplot\n",
    "\n",
    "labels = ['Block 1'] * 50 + ['Block 2'] * 50 + ['Block 3'] * 50\n",
    "\n",
    "plot = pairplot(X, labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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